Even in this age of the intrusion of market discipline into higher education, one area has remained remarkably resistant to close scrutiny. University admissions. Surprised I say this? After all, we will shortly be entering that bit of the year where it's the only news story in town. But bear with me. It is about time for the Office of Fair Trading to start sniffing around.

The Ucas system allows students to apply for up to five courses. From the point of the view of the universities, this is a sensible number. It keeps total numbers of applications down, while giving admissions tutors a bit of choice, at least for popular courses. But are the interests of applicants equally well served? How is it different from the Chamber of Commerce telling shoppers that they mustn't pop into more than five shops on their next visit to the high street? Why shouldn't an applicant apply for 10 courses, or, for that matter, to every university in the country?

Even more anomalous is the cosy little arrangement whereby a high-flying applicant has to choose between Oxford and Cambridge. The system simply will not allow an application to both, unless, apparently, you are a would-be organ scholar. Again, it is easy to see why Oxford and Cambridge like it, but really, there are lots of things in life one would like but can't have. Shouldn't our membership of the EU rule out this sort of cartel?

Despite Ucas's valiant but limited attempts, the admissions system is still stacked in favour of the university sector's convenience. And, to paraphrase Rousseau, the use we make of this convenience shows you how undeserving we are to have it.

As last week's white paper on higher education acknowledges, the admissions system is ripe for reform, although, as the white paper also demonstrates, reform can be for the worse as well as for the better. Here, the way to go is to change the power relationship so that the candidates make the final and most important decision. We could set up "post-qualification admissions" so that each candidate is given a national rank ordering on the basis of their exam results, test scores and other relevant factors. Universities can set out their minimum pre-requisites for each course in terms of subjects previously studied and necessary level of achievement. Then the applicant coming first on the national list has first pick of university and course, subject to meeting the special conditions, and then we go down the list until we run out of places.

Yes, I know this could be problematic for art school and so on, but we could work round that. And it would take a lot of effort to get the scoring right, if it were even possible. But a lot of arbitrary factors – such as whether your application arrived on the admissions tutor's desk on a sunny day, or whether you had brushed your teeth before interview – would disappear. And we might even find that we are compliant with competition law.

Years ago, if this had been suggested to me, I would have been appalled. The only way we could tell whether someone was suitable for my subject, I would have said with great confidence and authority, is by interviewing them. But increasingly I came to think that essentially an interview tests preparedness for interview. That tells you something, but not everything, and certainly not the main thing. I started meeting people I personally had rejected as undergraduates who had excelled elsewhere and gone on to do postgraduate work, and even to academic posts.

How can we tell whether the current system really selects the best candidates? Only by tracing the equally well qualified applicants we reject and see what happened to them. But of course, no university has access to that information. And even if we did, it would be hard to know how to interpret the figures.

For a while I have had the view that the undergraduate admissions system is a lottery masquerading as forensic science. But if it is a lottery, why not make it a fairer one, and, to declare my own interest, one that will be a lot less work for academics and university administrators?

• Jonathan Wolff is professor of philosophy at University College London. His column appears monthly